# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

33
NBA PLAYERS' SALARIES AND THE DRAFT

In chapter 9 we determined salaries for baseball players based on how many wins a player generated over and above the number of wins that would be achieved with a team of “replacement players.” Using the WINVAL point ratings we can use the same approach to come up with an estimate of a fair salary for an NBA player.

During the 2006–7 season the average team payroll was \$66 million. The minimum player salary was around \$400,000. We will define the point value of a “replacement player” as —6. This is the usual point value for a player in the bottom 10% of the league point values. A team made up of replacement players would lose by 5 × (6) = 30 points per game to an average NBA team. After noting that an average NBA team scored 98.7 points per game during 2006–7, we find that our team of replacement players would have a scoring ratio of 68.7/98.7 = .696. Using the Pythagorean Theorem as we did in chapter 1, we find that our team of replacement players would be expected to win a fraction

of their games. This means our team of replacement players would not win one game during an 82- game season.

Calculating a Fair Player Salary Based
on Minutes Played and Points Rating

During an 82- game season, an NBA team plays 82 × 48 = 3,936 minutes (excluding overtime). To win 41 games, the team would need a scoring ratio of 1, which means that for 3,936 × 5 = 19,680 minutes the team would have to play 6 points better per 48 minutes of player time than a team made up of replacement players. Define Points over Replacement Player (PORP) by player point rating—( — 6) = player point rating of + 6.

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